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arXiv 2024年

作者： Zeng, Hongbo Huang, Chuangxia Liu, Bingwen School of Mathematics and Statistics Changsha University of Science and Technology Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Hunan Changsha410114 China College of Data Science Jiaxing University Zhejiang Jiaxing314001 China

In this paper we investigate the iteration problem for several chaos in non-autonomous discrete system (X, f1,∞). Firstly, we prove that the Li-Yorke chaos of a non-autonomous discrete dynamical system is preserved under iterations when f1,∞ converges to f, which weakens the condition in the literature that f1,∞ uniformly converges to f . Besides, we prove that both DC2’ and Kato’s chaos of a non-autonomous discrete dynamical system are iteration invariants. Additionally, we give a sufficient condition for non-autonomous discrete dynamical system to be Li-Yorke chaos. Finally, we give an example to show that the DC3 of a non-autonomous discrete dynamical system is not inherited under iterations, which partly answers an open question proposed by Wu and Zhu(Chaos in a class of non-autonomous discrete systems, ***. 2013,26:431-436). Copyright © 2024, The Authors. All rights reserved.

关键词： Dynamical systems

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Artificial neural networking (ANN) analysis for heat and entropy generation in flow of non-Newtonian fluid between two rotating disks

Artificial neural networking (ANN) analysis for heat and ent...

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作者： Zhao, Tie-Hong Khan, M. Ijaz Chu, Yu-Ming Department of Mathematics Hangzhou Normal University Hangzhou311121 China Department of Mathematics and Statistics Riphah International University I-14 Islamabad44000 Pakistan Department of Mathematics Huzhou University Huzhou313000 China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Changsha410114 China

Mixed convection is a mechanism of heat transport in a thermodynamic system in which the motion of fluid particles is produced by gravity as well as external forces like fans, pumps, or any other devices. Such type of heat transport has a fruitful application in daily life due to reliable maintenance. In this regard, numerous researchers and analyst have focused on the importance of mixed convective flow to explore its different aspects, and frequent research articles are published in this area. In this work, mixed convective entropy optimized nanomaterial magnetohydrodynamics (MHD) flow of Ree-Eyring fluid is discussed between two rotating disks. The effects of porosity and velocity slip are considered. Both the disks are rotating with different angular frequency and stretching rates. modeling is performed for the energy equation subject to heat generation/absorption, dissipation, radiative heat flux, and Joule heating. Four types of irreversibilities are discussed, and total entropy rate is calculated. The obtained results are compared with past studies and found good agreement with them. The physical curiosity like skin friction and Sherwood and Nusselt numbers are numerically calculated. Series solutions are computed via homotopy method. Our obtained outcomes show that the velocity and temperature fields show contrast behavior against larger magnetic parameter. It is also noticed that the entropy rate and Bejan number have opposite behaviors against higher values of Weissenberg number. The entropy rate increases for higher Weissenberg number while Bejan number decays. © 2021 John Wiley & Sons, Ltd.

关键词： Activation energy

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Accurate adaptive deep learning method for solving elliptic problems

arXiv

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arXiv 2024年

作者： Ying, Jinyong Xie, Yaqi Li, Jiao Wang, Hongqiao School of Mathematics and Statistics HNP-LAMA Central South University Hunan Changsha410083 China School of Mathematics and Statistics Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Hunan Changsha410114 China

Deep learning method is of great importance in solving partial differential equations. In this paper, inspired by the failure-informed idea proposed by Gao ***. (SIAM Journal on Scientific Computing 45(4)(2023)) and as an improvement, a new accurate adaptive deep learning method is proposed for solving elliptic problems, including the interface problems and the convection-dominated problems. Based on the failure probability framework, the piecewise uniform distribution is used to approximate the optimal proposal distribution and an kernel-based method is proposed for efficient sampling. Together with the improved Levenberg-Marquardt optimization method, the proposed adaptive deep learning method shows great potential in improving solution accuracy. Numerical tests on the elliptic problems without interface conditions, on the elliptic interface problem, and on the convection-dominated problems demonstrate the effectiveness of the proposed method, as it reduces the relative errors by a factor varying from 102 to 104 for different cases. Copyright © 2024, The Authors. All rights reserved.

关键词： Numerical methods

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Study on fractional fejÉr-hadamard type inequalities associated with generalized exponentially convexity

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UPB Scientific Bulletin, Series A: Applied Mathematics and Physics 2021年第4期83卷 159-170页

作者： Farid, Ghulam Guran, Liliana Qiang, Xiaoli Chu, Yu-Ming Department of Mathematics COMSATS University Islamabad Attock Campus Pakistan Department of Pharmaceutical Sciences "Vasile Goldiş" Western University L. Rebreanu Street no. 86 Arad310048 Romania Institute of Computing Science and Technology Guangzhou University Guangzhou510006 China Department of Mathematics Huzhou University Huzhou313000 China Hunan Provincial Key Labo-ratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science & Technology Changsha410114 China

In this paper fractional integral inequalities of Fejér-Hadamard type for a generalized notion of convexity are established. A new generalization of convexity named exponentially (α, h − m)-convex function unifies exponentially (h − m)-convex, exponentially (α − m)-convex and exponentially (s, m)-convex functions. By using the generalized fractional integral operators involving Mittag-Leffler function via a monotonically increasing function we have obtained some fractional versions of Fejér-Hadamard inequality for the generalized convexity. The obtained results lead to many inequalities of Fejér-Hadamard and Hadamard type for well-known fractional integral operators and different kinds of convexities. © 2021, Politechnica University of Bucharest. All rights reserved.

关键词： mathematical operators

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Global Dynamics of Delay Differential Equations with Non-Monotone Bistable Nonlinearities and Time-Varying Delays

SSRN

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SSRN 2024年

作者： Huang, Chuangxia Ding, Xiaodan Yu, Jianshe College of Science Hunan University of Science and Engineering Hunan Yongzhou425199 China School of Mathematics and Statistics Changsha University of Science and Technology Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Hunan Changsha410114 China Guangzhou Center for Applied Mathematics Guangzhou University Guangzhou510006 China

In this paper, we consider a class of non-autonomous delay differential equations incorporating non-monotone bistable nonlinearities and multiple time-varying delays, where the zero equilibrium point may coexist with at most two positive equilibrium points. We aim to provide a fairly complete description of the global dynamics, including global asymptotic stability, semi-stability, bi-stability, and basins of attraction. Characterizing the attractiveness of a positive equilibrium point is a very signiﬁcant challenge even in the case of the non-linear initial values crossing this equilibrium point. Here, we combine the differential inequality technique, the ﬂuctuation lemma and the domain decomposition strategy to overcome the difﬁculties. The obtained results improve and generalize some existing ones. © 2024, The Authors. All rights reserved.

关键词： Asymptotic stability

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modeling and numerical analysis of nanoliquid (titanium oxide, graphene oxide) flow viscous fluid with second order velocity slip and entropy generation

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Chinese Journal of Chemical engineering 2021年第3期34卷 17-25页

作者： M.Ijaz Khan Seifedine Kadry Yuming Chu M.Waqas Department of Mathematics Riphah International UniversityFaisalabad CampusFaisalabad 38000Pakistan Department of Mathematics and Computer Science Beirut Arab UniversityBeirutLebanon Department of Mathematics Huzhou UniversityHuzhou 313000China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science&TechnologyChangsha 410114China NUTECH School of Applied Sciences and Humanities National University of TechnologyIslamabad 44000Pakistan

The prime objective of the present communication is to examine the entropy-optimized second order velocity slip Darcy–Forchheimer hybrid nanofluid flow of viscous material between two rotating *** conducting flow is considered and saturated through Darcy–Forchheimer *** the disks are rotating with different angular frequencies and stretches with different *** graphene oxide and titanium dioxide are considered for hybrid nanoparticles and water as a continuous phase *** heating,heat generation/absorption and viscous dissipation effects are incorporated in the mathematical modeling of energy ***,binary chemical reaction with activation energy is *** total entropy rate is calculated in the presence of heat transfer irreversibility,fluid friction irreversibility,Joule heating irreversibility,porosity irreversibility and chemical reaction irreversibility through thermodynamics second *** nonlinear governing equations are first converted into ordinary differential equations through implementation of appropriate similarity transformations and then numerical solutions are calculated through Built-in-Shooting *** of sundry flow variables on the entropy generation rate,velocity,concentration,Bejan number,temperature are discussed graphically for both graphene oxide and titanium dioxide hybrid *** engineering interest like skin friction coefficient and Nusselt number are computed numerically and presented through *** is noticed from the obtained results that entropy generation rate and Bejan number have similar effects versus diffusion *** entropy generation rate is more against the higher Brinkman number.

关键词： Darcy-Forchheimer porous medium Titanium dioxide and graphene oxide nanoparticles Second order velocity slip Convective boundary condition Activation energy Heat generation/absorption

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O(t^(-β))-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

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Acta Mathematica Scientia 2022年第4期42卷 1273-1292页

作者： Anbalagan PRATAP Ramachandran RAJA Jinde CAO Chuangxia HUANG Jehad ALZABUT Ovidiu BAGDASAR Department of Mathematics Alagappa UniversityKaraikudi 630004India Ramanujan Centre for Higher Mathematics Alagappa UniversityKaraikudi 630004India School of Mathematics Southeast UniversityNanjing 211189China Yonsei Frontier Lab Yonsei UniversitySeoul03722South Korea Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and TechnologyChangsha410114China Department of Mathematics and General Sciences Prince Sultan UniversityRiyadh 12435Saudi Arabia Department of Electronics Computing and MathematicsUniversity of DerbyUnited Kingdom

This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical *** designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control ***,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.

关键词： O(t^(-β))-synchronization asymptotic synchronization BAM neural networks fractional order state feedback control law

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Exit identities for diusion processes observed at Poisson arrival times

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Frontiers of Mathematics in China 2020年第3期15卷 507-528页

作者： Yingqiu LI Ye CHEN Shilin WANG Zhaohui PENG School of Mathematics and Statistics Changsha University of Science and TechnologyChangsha 410004China College of Mathematics and Physics Hunan University of Arts and ScienceChangde 415000China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and TechnologyChangsha 410004China

For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson *** results are expressed in terms of solutions to the ... 详细信息

关键词： Time-homogeneous diffusion process exit problem Poisson arrival time Brownian motion

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Stability analysis and modeling for the three-dimensional Darcy-Forchheimer stagnation point nanofluid flow towards a moving surface

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Applied Mathematics and Mechanics(English Edition) 2021年第3期42卷 357-370页

作者： Yuming CHU M.I.KHAN M.I.U.REHMAN S.KADRY S.QAYYUM M.WAQAS Department of Mathematics Huzhou UniversityHuzhou 313000Zhejiang ProvinceChina Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science&TechnologyChangsha 410114China Department of Mathematics Riphah International UniversityFaisalabad CampusFaisalabad 38000Pakistan Department of Mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan Department of Mathematics and Computer Science Beirut Arab UniversityBeirut 11072809Lebanon NUTECH School of Applied Sciences and Humanities National University of TechnologyIslamabad 44000Pakistan

In this research,the three-dimensional(3D)steady and incompressible laminar Homann stagnation point nanofluid flow over a porous moving surface is *** disturbance in the porous medium has been characterized by the Darcy-Forchheimer *** slip for viscous fluid is *** energy equation is organized in view of radiative heat flux which plays an important role in the heat transfer *** governing flow expressions are first altered into first-order ordinary ones and then solved numerically by the shooting *** solutions are obtained for the velocity,skin friction coefficient,temperature,and Nusselt number subject to sundry flow parameters,magnetic parameter,Darcy-Forchheimer number,thermal radiation parameter,suction parameter,and dimensionless slip *** this research,the main consideration is given to the engineering interest like skin friction coefficient(velocity gradient or surface drag force)and Nusselt number(temperature gradient or heat transfer rate)and discussed numerically through *** conclusion,it is noticed from the stability results that the upper branch solution(UBS)is more reliable and physically stable than the lower branch solution(LBS).

关键词： viscous slip Darcy-Forchheimer relation thermal radiation stagnation point flow dual solution heat generation/absorption stability result

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Path Planning for Underwater Glider Based on Ant Colony Algorithm Guided by Artificial Potential Field 6

Path Planning for Underwater Glider Based on Ant Colony Algo...

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6th International Conference on Communication, Image and Signal Processings, CCISP 2021

作者： Jin, Xiantao Huang, Chuangxia Bao, Changchun School of Mathematics and Statistics Changsha University of Science and Technology College of Meteorology and Oceanography National University of Defense Technology Changsha410073 China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Changsha410114 China College of Meteorology and Oceanography National University of Defense Technology Changsha410073 China

ISBN: (纸本)9781665432795

This paper studies the path planning of underwater gliders in a global static environment, and proposes an improved algorithm based on ant colony algorithm, which eliminates the problem of slow convergence due to the lack of initial pheromone in path planning of ant colony algorithm. Firstly, according to the operating characteristics of the glider, the grid method is used to model the known marine environment;Secondly, the improved artificial potential field method is introduced to construct the heuristic information function to speed up the convergence speed of the ant colony algorithm;Finally, the ant colony algorithm is used to search Path, improve the original pheromone update rule of the ant colony algorithm. The simulation results show that the algorithm in this paper is effective and superior. © 2021 IEEE.

关键词： Motion planning

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